Question

Tìm tổng: S=1+2+2^2+2^3+2^4+2^5+............+2^49+2^50

Answer 1

\(S=1+2+2^2+...+2^{50}\)

\(2S=2.1+2.2+2^2.2+...+2^{50}.2\)

\(2S=2+2^2+2^3+...+2^{51}\)

\(2S-S=S=\left(2+2^2+2^3+...+2^{51}\right)-\left(1+2+2^2+...+2^{50}\right)\)

\(\Rightarrow S=2^{51}-1\)

Answer 2

2S - S = ( 2+2^2 + 2^3 +....+ 2^51 ) - (1+2+2^2+...+2^50) 
S= 1 + 2^51
Vậy nha